Answer:
[tex] c = 25[/tex]
Step-by-step explanation:
Given :-
And we need to find out the value of c for which the given trinomial is a perfect square. On looking at the given expression all the terms are having positive signs before them .So we can rewrite it on the basis of ,
Identity :-
[tex]\implies (a+b)^2=a^2+b^2+2ab[/tex]
Let's try to set the equation on this Identity .
The firsr term is 9x² . We can write it as ,
[tex]\implies 9x^2=(3x)^2[/tex]
Hence the middle term here should contain 3 and 2 as their factors. Let's Break the middle term .
[tex]\implies 30x = 2.3x.5 [/tex]
Therefore in order to make the whole expression as perfect square 5² must be replaced by c . The expression would become ,
[tex]\implies 9x^2+30x + 5^2 \\\\\implies (3x)^2+2.3x.5 +5^2\\\\\implies (3x+5)^2[/tex]
Hence the value of c should be 25 .
